It is well-known that in the conventional semiconductor power devices, the reverse voltage applied across the n.sup.+ -region(s) and p.sup.+ -region(s) is sustained by a lightly doped semiconductor layer, called hereafter as voltage sustaining layer. For high voltage power devices, the on-resistance (or the on-voltage) is also dominantly determined by the voltage sustaining layer. The breakdown voltage mainly depends on the doping concentration and the thickness of the layer. The lower the concentration is and/or the larger the thickness is, the higher the breakdown voltage is, but the larger also the on-resistance (or the on-voltage) is. One of the most important problems of many power devices, especially of the majority devices like VVMOS, VDMOS and RMOS, is to get both high breakdown voltage and low on-resistance. For example, in the most advanced power MOSFET, RMOS(or UMOS), shown schematically in FIG. 1, the voltage sustaining layer is an n.sup.+ -epi-layer, the theoretical limit of the on-resistance in unit area Ron is Ron=7.4.times.10.sup.-9 V.sub.B.sup.2.5 [.OMEGA..cm.sup.2 ], where V.sub.B is the breakdown voltage of the device. For references of the relation between Ron and V.sub.B see: [1] C. F. Wheately. G. M. Dolny. Solid-State Technology, November 1985.pp 121-128; [2] C.Hu. IEEE Trans. Electron Devices, Vol. ED-26, NO. 3.pp. 243-246(1979); [3] D. Ueda, H. Takagi, G. Hano. IEEE Trans. Electron Devices, Vol. ED-34.pp 926-930 (1987); (4) H. R. Chang. R. D. Black et al. IEEE Trans. Electron Devices, Vol. ED-34, pp. 2329-2333 (1987). Also, see a U.S. patent--[5] Goodman et al. U.S. Pat. No. 4,366,495, Dec. 23, 1982, where improvement has been made to reduce the practical on-resistance of the VDMOS, however, the devices disclosed in Goodman et al. retain the relation between Ron and V.sub.B. This relation has been an obstacle for making high performance power devices. Moreover. Ron stated above refers to the conduction area of the voltage sustaining layer, but practically, there exists always some areas which do not contribute very much to the conduction. The examples of such areas are: the area under the source-body in a vertical MOSFET; the area under the base contact of the bipolar transistors.